Att C - ASEC 2020 - S&A

Source of the Data and Accuracy of the Estimates for the
2020 Annual Social and Economic Supplement Microdata File

Attachment C

SOURCE OF THE DATA
The data in this microdata file and the estimates in the reports Income and Poverty in the
United States: 2019, Health Insurance Coverage in the United States: 2019, and The
Supplemental Poverty Measure: 2019 come from the 2020 1 Annual Social and Economic
Supplement (ASEC) of the Current Population Survey (CPS). 2 The U.S. Census Bureau
conducts the CPS ASEC over a 3-month period in February, March, and April, with most of
the data collection occurring in the month of March. The CPS ASEC uses two sets of
questions, the basic CPS and a set of supplemental questions. The CPS, sponsored jointly by
the Census Bureau and the U.S. Bureau of Labor Statistics, is the country’s primary source
of labor force statistics for the entire population. The Census Bureau and the U.S. Bureau of
Labor Statistics also jointly sponsor the CPS ASEC.
Basic CPS. The monthly CPS collects primarily labor force data about the civilian
noninstitutionalized population living in the United States. The institutionalized
population, which is excluded from the universe, consists primarily of the population in
correctional institutions and nursing homes (98 percent of the 4.0 million institutionalized
people in the 2010 Census). Starting in August 2017, college and university dormitories
were also excluded from the universe because most of the residents had usual residences
elsewhere. Interviewers ask questions concerning labor force participation of each
member 15 years old and older in sample households. Typically, the week containing the
nineteenth of the month is the interview week. The week containing the twelfth is the
reference week (i.e., the week about which the labor force questions are asked).
The CPS uses a multistage probability sample based on the results of the decennial census,
with coverage in all 50 states and the District of Columbia. The sample is continually
updated to account for new residential construction. When files from the most recent
decennial census become available, the Census Bureau gradually introduces a new sample
design for the CPS.

Every ten years, the CPS first-stage sample is redesigned 3 reflecting changes based on the
most recent decennial census. In the first stage of the sampling process, primary sampling
units (PSUs) 4 were selected for sample. In the 2000 design, the United States was divided
1

2
3
4

For clarity and consistency throughout this report, the term “collection year” is the year the data is
collected (in this case, 2020), and “data year” is the year about which the data are obtained (in this case,
2019). 2020 CPS ASEC asks questions of data year 2019, 2019 CPS ASEC asks questions of data year
2018, etc.
Portions of the health insurance data in the report are based on the American Community Survey (ACS).
Please refer to the ACS Source and Accuracy Statement in U.S. Census Bureau (2019c).
For detailed information on the 2010 sample redesign, please see Bureau of Labor Statistics (2014).
The PSUs correspond to substate areas (i.e., counties or groups of counties) that are geographically
contiguous.

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into 2,025 PSUs. These were then grouped into 824 strata and one PSU was selected for
sample from each stratum. In the 2010 sample design, the United States was divided into
1,987 PSUs. These PSUs were then grouped into 852 strata. Within each stratum, a single
PSU was chosen for the sample, with its probability of selection proportional to its
population as of the most recent decennial census. In the case of strata consisting of only
one PSU, the PSU was chosen with certainty.
In April 2014, the Census Bureau began phasing out the 2000 sample and replaced it with
the 2010 sample, creating a mixed sampling frame. Two simultaneous changes occurred
during this phase-in period. First, within the PSUs selected for both the 2000 and 2010
designs, sample households from the 2010 design gradually replaced sample households
from the 2000 design. Second, new PSUs selected for only the 2010 design gradually
replaced outgoing PSUs selected for only the 2000 design. By July 2015, the new 2010
sample design was completely implemented and the sample came entirely from the 2010
redesigned sample.

Approximately 70,300 sampled addresses were selected from the sampling frame for the
basic CPS. Based on eligibility criteria, ten percent of these sampled addresses were sent
directly to computer-assisted telephone interviewing (CATI). The remaining sampled
addresses were assigned to interviewers for computer-assisted personal interviewing
(CAPI). 5 Of all addresses in sample, about 59,700 were determined to be eligible for
interview. Interviewers obtained interviews at about 43,600 of the housing units at these
addresses. 6 Noninterviews occur when the occupants are not found at home after repeated
calls or are unavailable for some other reason. Table 1 summarizes historical changes in
the CPS design.
The 2020 Annual Social and Economic Supplement. In addition to the basic CPS
questions, interviewers asked supplementary questions for the CPS ASEC. They asked
these questions of the civilian noninstitutionalized population and also of military
personnel who live in households with at least one other civilian adult. The additional
questions covered the following topics:
•
•
•

5

6

G-2

Household and family characteristics.
Marital status.
Geographic mobility.

For further information on CATI and CAPI and the eligibility criteria, please see U.S. Census Bureau
(2019e).
Due to government restrictions/health and safety concerns stemming from the spread of COVID-19,
March CPS interviewing was impacted. Interviewing began Sunday, March 15th. On Friday, March 20th,
personal visits with respondents were halted nationwide, resulting in telephone contacts only.
Additionally, both CATI contact centers were closed as of Friday, March 20th. All cases remaining in CATI
for ASEC follow-up were closed out and sent in to headquarters. Therefore, no CATI follow-up occurred
after March 20th. These procedural changes resulted in higher nonresponse for both the basic CPS and
the ASEC Supplement. For additional information on the impacts of COVID-19 on the CPS ASEC, please
see Subsection “Impact of the Coronavirus Pandemic” within Section “Comparability of Data”.

SOURCE & ACCURACY

•
•
•
•
•
•

Foreign-born population.
Income from the previous calendar year.
Work status/occupation.
Health insurance coverage.
Program participation.
Educational attainment.

Including the basic CPS sample, approximately 91,500 addresses were in sample for the
CPS ASEC. About 79,400 sampled addresses were determined to be eligible for interview,
and about 60,400 interviews were conducted (see Table 1).

The additional sample for the CPS ASEC provides more reliable data than the basic CPS for
Hispanic households, non-Hispanic minority households, and non-Hispanic White
households with children 18 years or younger. These households were identified for
sample from previous months and the following April. For more information about the
households eligible for the CPS ASEC, please refer to U.S. Census Bureau (2019e).

Table 1. Description of the March Basic Current Population Survey and Annual Social and
Economic Supplement Sample Cases
Number Basic CPSB sampled addresses
Total (CPS ASECC/ADSD + basic
of
eligible
CPS) sampled addresses eligible
Time period
sample
Interviewed
Not interviewed Interviewed Not interviewed
PSUsA
2020
852
43,600
16,100
60,400
19,000
2019
852
48,900
11,100
68,300
13,600
2018
852
50,800
9,900
67,900
11,500
2017
852
52,400
9,300
70,000
10,900
2016
852
52,000
9,100
69,500
10,600
2015
852
52,900
8,200
74,300
10,300
E
2014 Redesign
824
17,200
2,200
22,700
2,600
F
2014 Traditional
824
35,500
4,600
51,500
5,800
2014
824
52,700
6,800
--2013
824
52,900
6,400
75,500
7,700
2012
824
53,300
5,800
75,100
7,200
2011
824
53,400
5,300
75,900
6,500
2010
824
54,100
4,600
77,000
5,700
2009
824
54,100
4,600
76,200
5,700
2008
824
53,800
5,100
75,900
6,400
2007
824
53,700
5,600
75,500
7,100
2006
824
54,000
5,400
76,000
7,100
G
2005
754/824
54,400
5,700
76,500
7,500
2004
754
55,000
5,200
77,700
7,000
2003
754
55,500
4,500
78,300
6,800
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Time period

Number Basic CPSB sampled addresses
of
eligible
sample
Interviewed Not interviewed
PSUsA

Total (CPS ASECC/ADSD + basic
CPS) sampled addresses eligible
Interviewed

Not interviewed

2002
2001
2000
1999
1998
1997
1996
1995
1990 to 1994
1989
1986 to 1988
1985
1982 to 1984
1980 to 1981
1977 to 1979
1976
1973 to 1975
1972
1967 to 1971
1963 to 1966
1960 to 1962
1959

754
55,500
4,500
78,300
6,600
754
46,800
3,200
49,600
4,300
754
46,800
3,200
51,000
3,700
754
46,800
3,200
50,800
4,300
754
46,800
3,200
50,400
5,200
754
46,800
3,200
50,300
3,900
754
46,800
3,200
49,700
4,100
792
56,700
3,300
59,200
3,800
729
57,400
2,600
59,900
3,100
729
53,600
2,500
56,100
3,000
729
57,000
2,500
59,500
3,000
H629/729
57,000
2,500
59,500
3,000
629
59,000
2,500
61,500
3,000
629
65,500
3,000
68,000
3,500
614
55,000
3,000
58,000
3,500
624
46,500
2,500
49,000
3,000
461
46,500
2,500
49,000
3,000
I449/461
45,000
2,000
45,000
2,000
449
48,000
2,000
48,000
2,000
357
33,400
1,200
33,400
1,200
333
33,400
1,200
33,400
1,200
330
33,400
1,200
33,400
1,200
Source: U.S. Census Bureau, Current Population Survey, 1959-2020 Annual Social and Economic Supplement.
A
PSUs are primary sampling units.
B
CPS is the Current Population Survey.
C
CPS ASEC is the Annual Social and Economic Supplement of the Current Population Survey.
D
The CPS ASEC was referred to as the Annual Demographic Supplement (ADS) until 2002.
E
The 2014 CPS ASEC Redesign indicates the subsample of the basic CPS households which received the
redesigned ASEC questionnaire incorporating new income and health insurance questions.
F
The 2014 CPS ASEC Traditional indicates the subsample of the basic CPS households which received the
the same ASEC questionnaire that was used in the 2013 CPS ASEC.
G
The Census Bureau redesigned the CPS following the Census 2000. During phase-in of the new design,
addresses from the new and old designs were in the sample.
H
The Census Bureau redesigned the CPS following the 1980 Decennial Census of Population and Housing.
I
The Census Bureau redesigned the CPS following the 1970 Decennial Census of Population and Housing.

Estimation Procedure. This survey’s estimation procedure adjusts weighted sample
results to agree with independently derived population controls of the civilian
noninstitutionalized population of the United States, each state, and the District of
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SOURCE & ACCURACY

Columbia. These population controls 7 are prepared monthly as part of the Census Bureau’s
Population Estimates Program.

The population controls for the nation are distributed by demographic characteristics in
two ways:
•
•

Age, sex, and race (White alone, Black alone, and all other groups combined).
Age, sex, and Hispanic origin.

The population controls for the states are distributed by:
•
•
•

Race (Black alone and all other race groups combined).
Age (0-15, 16-44, and 45 and over).
Sex.

The independent estimates by age, sex, race, and Hispanic origin, and for states by selected
age groups and broad race categories, are developed using the basic demographic
accounting formula whereby the population from the 2010 Census data is updated using
data on the components of population change (births, deaths, and net international
migration) with net internal migration as an additional component in the state population
controls.
The net international migration component of the population controls includes:
•
•
•
•

Net international migration of the foreign born;
Net migration between the United States and Puerto Rico;
Net migration of natives to and from the United States; and
Net movement of the Armed Forces population to and from the United States.

Because the latest available information on these components lags behind the survey date,
it is necessary to make short-term projections of these components to develop the estimate
for the survey date.
The estimation procedure of the CPS ASEC includes a further adjustment to give married
and unmarried partners the same weight.

ACCURACY OF THE ESTIMATES
A sample survey estimate has two types of error: sampling and nonsampling. The accuracy
of an estimate depends on both types of error. The nature of the sampling error is known
given the survey design; the full extent of the nonsampling error is unknown.
7

For additional information on population controls, including details on the demographic characteristics
used and net international components, please see Chapters 1-3 and Appendix: History of the Current
Population Survey of U.S. Census Bureau (2019e).

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Sampling Error. Since the CPS estimates come from a sample, they may differ from figures
from an enumeration of the entire population using the same questionnaires, instructions,
and enumerators. For a given estimator, the difference between an estimate based on a
sample and the estimate that would result if the sample were to include the entire
population is known as sampling error. Standard errors, as calculated by methods
described in “Standard Errors and Their Use,” are primarily measures of the magnitude of
sampling error. However, the estimation of standard errors may include some
nonsampling error.
Nonsampling Error. For a given estimator, the difference between the estimate that
would result if the sample were to include the entire population and the true population
value being estimated is known as nonsampling error. There are several sources of
nonsampling error that may occur during the development or execution of the survey. It
can occur because of circumstances created by the interviewer, the respondent, the survey
instrument, or the way the data are collected and processed. Some nonsampling errors,
and examples of each, include:
•

•
•
•
•

Measurement error: The interviewer records the wrong answer, the respondent
provides incorrect information, the respondent estimates the requested.
information, or an unclear survey question is misunderstood by the respondent.
Coverage error: Some individuals who should have been included in the survey
frame were missed.
Nonresponse error: Responses are not collected from all those in the sample or
the respondent is unwilling to provide information.
Imputation error: Values are estimated imprecisely for missing data.
Processing error: Forms may be lost, data may be incorrectly keyed, coded, or
recoded, etc.

To minimize these errors, the Census Bureau applies quality control procedures during all
stages of the production process including the design of the survey, the wording of
questions, the review of the work of interviewers and coders, and the statistical review of
reports.

Answers to questions about money income often depend on the memory or knowledge of
one person in a household. Recall problems can cause underestimates of income in survey
data because it is easy to forget minor or irregular sources of income. Respondents may
also misunderstand what the Census Bureau considers money income or may simply be
unwilling to answer these questions correctly because the questions are considered too
personal. For more details, please see Appendix C of U.S. Census Bureau (1993).
Two types of nonsampling error that can be examined to a limited extent are nonresponse
and undercoverage.
Nonresponse. The effect of nonresponse cannot be measured directly, but one indication
of its potential effect is the nonresponse rate. For the cases eligible for the 2020 ASEC, the
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basic CPS household-level unweighted nonresponse rate was 23.9 percent. The householdlevel unweighted nonresponse rate for the ASEC was an additional 19.7 percent. These two
nonresponse rates lead to a combined supplement unweighted nonresponse rate of 38.9
percent. 8
In accordance with Census Bureau and Office of Management and Budget Quality
Standards, the Census Bureau will conduct an analysis to assess nonresponse bias in the
2020 CPS ASEC.
Responses are made up of complete interviews and sufficient partial interviews. A
sufficient partial interview is an incomplete interview in which the household or person
answered enough of the questionnaire for the supplement sponsor to consider the
interview complete. The remaining supplement questions may have been edited or
imputed to fill in missing values. Insufficient partial interviews are considered to be
nonrespondents. Refer to the supplement overview attachment in the technical
documentation for the specific questions deemed critical by the sponsor as necessary to
answer in order to be considered a sufficient partial interview.

As a result of sufficient partial interviews being considered responses, individual
items/questions have their own response and refusal rates. As part of the nonsampling
error analysis, the item response rates, item refusal rates, and edits are reviewed. For the
CPS ASEC, the unweighted item refusal rates range from 0.0 percent to 3.3 percent. The
unweighted item allocation rates range from 23.3 percent to 74.1 percent.

Undercoverage. The concept of coverage with a survey sampling process is defined as the
extent to which the total population that could be selected for sample “covers” the survey’s
target population. Missed housing units and missed people within sample households
create undercoverage in the CPS. Overall CPS undercoverage for March 2020 is estimated
to be about ten percent. CPS coverage varies with age, sex, and race. Generally, coverage is
higher for females than for males and higher for non-Blacks than for Blacks. This
differential coverage is a general problem for most household-based surveys.
The CPS weighting procedure mitigates bias from undercoverage, but biases may still be
present when people who are missed by the survey differ from those interviewed in ways
other than age, race, sex, Hispanic origin, and state of residence. How this weighting
procedure affects other variables in the survey is not precisely known. All of these
considerations affect comparisons across different surveys or data sources.

A common measure of survey coverage is the coverage ratio, calculated as the estimated
population before poststratification divided by the independent population control. Table
2 shows March 2020 CPS coverage ratios by age and sex for certain race and Hispanic
groups. The CPS coverage ratios can exhibit some variability from month to month.
8

Because the ASEC is at the household level, the overall/combined ASEC response rate is a product of the
basic CPS response rate and the ASEC response rate.

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Table 2. Current Population Survey Coverage Ratios: March 2020
Total
White alone
Black alone Residual raceA

HispanicB

Age
All
Male Female Male Female Male Female Male Female Male Female
group people
0-15 0.85
0.85
0.86
0.89
0.90
0.72
0.69
0.80
0.83
0.77
0.78
16-19 0.83
0.84
0.83
0.87
0.86
0.69
0.68
0.80
0.84
0.81
0.81
20-24 0.75
0.76
0.74
0.80
0.76
0.63
0.63
0.68
0.76
0.80
0.73
25-34 0.79
0.76
0.82
0.81
0.86
0.51
0.67
0.79
0.76
0.69
0.76
35-44 0.88
0.86
0.91
0.90
0.94
0.67
0.80
0.81
0.83
0.75
0.85
45-54 0.90
0.89
0.92
0.90
0.95
0.80
0.81
0.88
0.90
0.81
0.91
55-64 0.98
0.97
0.98
0.99
1.01
0.84
0.92
0.94
0.86
0.89
0.90
65+
1.02
1.03
1.01
1.06
1.04
0.88
0.95
0.87
0.77
0.92
0.92
15+
0.90
0.89
0.91
0.92
0.94
0.71
0.80
0.83
0.81
0.79
0.84
0+
0.89
0.88
0.90
0.92
0.94
0.71
0.77
0.82
0.82
0.78
0.82
Source: U.S. Census Bureau, Current Population Survey, March 2020.
A
The Residual race group includes cases indicating a single race other than White or Black, and cases
indicating two or more races.
B
Hispanics may be any race.
Note: For a more detailed discussion on the use of parameters for race and ethnicity, please see the
“Generalized Variance Parameters” section.

Comparability of Data. Data obtained from the CPS and other sources are not entirely
comparable. This is due to differences in interviewer training and experience and in
differing survey processes. These differences are examples of nonsampling variability not
reflected in the standard errors. Therefore, caution should be used when comparing
results from different sources.

Data users should be aware that estimates in the reports, Income and Poverty in the United
States: 2019, Health Insurance Coverage in the United States: 2019, and The Supplemental
Poverty Measure: 2019, use the internal CPS ASEC file. The Census Bureau must keep
survey responses confidential, so disclosure avoidance techniques are applied to files prior
to public release. Therefore, some estimates using the microdata files may differ from the
estimates provided in the reports.
Caution should be used when comparing estimates of the Hispanic population over time.
No independent population control totals for people of Hispanic origin were used before
1985.

Caution should also be used when comparing CPS ASEC results from different years.
Below, more detail is provided on several reasons for caution when comparing estimates
across years.
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Impact of the Coronavirus Pandemic. Data users should exercise caution when comparing
estimates for data year 2019 from the reports or from the microdata files to those from
previous years due to the effects that the coronavirus (COVID-19) had on interviewing and
response rates. Interviewing for the March CPS began on March 15th. In order to protect
the health and safety of Census Bureau staff and respondents, the survey suspended inperson interviewing and closed the two CATI contact centers on March 20th. For the rest
of March and through April, the Census Bureau continued to attempt all interviews by
phone. For those whose first month in the survey was March or April, the Census Bureau
used vendor-provided telephone numbers associated with the sample address.

While the Census Bureau went to great lengths to complete interviews by telephone, the
response rate for the CPS basic household survey in March 2020 was 73 9 percent, about 10
percentage points lower than in preceding months and the same period in 2019. Further,
as the Bureau of Labor Statistics (2020) stated in their Frequently Asked Questions
accompanying the April 3rd release of The Employment Situation for March 2020,
“Response rates for households normally more likely to be interviewed in person were
particularly low. The response rate for households entering the sample for their first
month was over 20 percentage points lower than in recent months, and the rate for those
in the fifth month was over 10 percentage points lower.”

The effect of changes in collection methods continued to be felt into April. The response
rate for households entering the sample for their first month of interviewing was especially
low. The unweighted April response rate for these households, which would normally have
been interviewed in person, was over 30 percentage points lower than the average for the
12 months ending in February. Because the April ASEC selects households only from those
in their first or fifth contact, the lower response rate translates into fewer potential ASEC
households.

9

This value differs from the response rate obtained using the values in the “Nonresponse” section because
this value is specifically for March CPS whereas the values in the “Nonresponse” section are for the full
CPS sample that was eligible for ASEC.

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Figure 1: Unweighted Current Population Survey Monthly Response Rates for May 2010
through April 2020

Source: U.S. Census Bureau, Current Population Survey, internal data files, May 2010-April 2020.

The CPS ASEC response rate is complicated by the different months and samples that feed
into the survey. Further, it includes an adjustment factor to account for those who
responded to the basic survey but refused to answer the supplement. The Census Bureau
estimates that the unweighted combined supplement response rate was 61.1 percent in
2020, down from 67.6 percent in 2019.

The change from conducting first interviews in person to making first contacts by
telephone only is a contributing factor to the lower response rates. Further, it is likely that
the characteristics of people for whom a telephone number was found may be
systematically different from the people for whom the Census Bureau was unable to obtain
a telephone number. While the Census Bureau creates weights designed to adjust for
nonresponse and to control weighted counts to independent population estimates by age,
sex, race, and Hispanic origin, the magnitude of the increase in (and differential nature of)
nonresponse related to the pandemic likely reduced their effectiveness. Using
administrative data, Census Bureau researchers have documented that there are more (and
larger) differences between respondents and nonrespondents in 2020 than in the prior
three years. Of particular interest for the estimates in the ASEC reports are the differences
in median income and educational attainment, indicating that respondents in 2020 had
relatively higher income and were more educated than nonrespondents. 10
Change in Processing System. Data users should exercise caution when comparing estimates
from the CPS ASEC for data years 2019 and 2018 to estimates from earlier years. An updated
data processing system was implemented beginning with data year 2018 estimates. This
system introduced demographic edit changes to account for same-sex couples, revised
procedures for editing income and health insurance variables, and added several new income
and health insurance variables. Changes to the editing procedures encompassed both changes
to the resolution of logically inconsistent data and changes to the imputation methods. The
10

For additional information, please see Rothbaum & Bee (2020).

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2019 and 2020 CPS ASEC estimates for data years 2018 and 2019 can be compared to the
2018 CPS ASEC Bridge Files11, which contain data year 2017 estimates, and to the 2017 CPS
ASEC Research Files12, which contain estimates for data year 2016. The 2017 Research File
and the 2018 Bridge File both use the new processing system and serve as a bridge between
the legacy production files and the updated processing system. Data users should be aware
that the estimates from the 2017 and 2018 CPS ASEC Files for data years 2016 and 2017 using
the legacy processing system are not directly comparable to 2019 CPS ASEC and 2020 CPS
ASEC estimates.
Change in Questionnaire. In 2014, the ASEC questionnaire was resigned to incorporate new
income and health insurance questions. Due to the differences in measurement, health
insurance estimates for 2014-2017 CPS ASEC for data years 2013-2016 are not directly
comparable to health insurance estimates for previous years.13 For income and poverty
estimates, when survey changes had statistically significant impacts, comparisons should be
made by adjusting historical published estimates to approximate the magnitude of those
impacts.14

Change in Census-Based Controls. Data users should exercise caution when comparing
estimates for 2019 from the microdata file or from the ASEC reports, Income and Poverty in
the United States: 2019 and Health Insurance Coverage in the United States: 2019 (which
reflect 2010 Census-based controls), with estimates from the microdata files or ASEC
Reports for 2001 to 2010 (from March 2002 CPS to March 2011 CPS), which reflect 2000
Census-based controls, and to 1993 to 2000 (from March 1994 CPS to March 2001 CPS),
which reflect 1990 Census-based controls. Ideally, the same population controls should be
used when comparing any estimates. In reality, the use of the same population controls is
not practical when comparing trend data over a period of 10 to 20 years. Thus, when it is
necessary to combine or compare data based on different controls or different designs,
data users should be aware that changes in weighting controls or weighting procedures
could create small differences between estimates.
Microdata files from previous years reflect the latest available census-based controls.
Although the most recent change in population controls had relatively little impact on
summary measures such as averages, medians, and percentage distributions, it did have a
significant impact on levels. For example, use of 2010 Census-based controls results in
about a 0.2 percent increase from the 2000 Census-based controls in the civilian
noninstitutionalized population and in the number of families and households. Thus,
estimates of levels for data collected in 2012 and later years will differ from those for
earlier years by more than what could be attributed to actual changes in the population.
11
12
13
14

For additional information on the 2018 CPS ASEC Bridge Files, please see the Documentation and User
Notes in US Census Bureau (2019b).
For additional information on the 2017 CPS ASEC Research Files, please see the Documentation and User
Notes in US Census Bureau (2019a).
For more information, see U.S. Census Bureau (2019f).
For more details on the adjustment for these comparisons, see U.S. Census Bureau (2019g).

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These differences could be disproportionately greater for certain population subgroups
than for the total population.

Users should also exercise caution because of changes caused by the phase-in of the 2010
Census files (see “Basic CPS”). 15 During this time period, CPS data were collected from
sample designs based on different censuses. Two features of the new CPS design have the
potential of affecting estimates: (1) the temporary disruption of the rotation pattern from
August 2014 through June 2015 for a comparatively small portion of the sample and (2)
the change in sample areas. Most of the known effect on estimates during and after the
sample redesign will be the result of changing from 2000 to 2010 geographic definitions.

Research has shown that the national-level estimates of the metropolitan and
nonmetropolitan populations should not change appreciably because of the new sample
design. However, users should still exercise caution when comparing metropolitan and
nonmetropolitan estimates across years with a design change, especially at the state level.
A Nonsampling Error Warning. Since the full extent of the nonsampling error is
unknown, one should be particularly careful when interpreting results based on small
differences between estimates. The Census Bureau recommends that data users
incorporate information about nonsampling errors into their analyses, as nonsampling
error could impact the conclusions drawn from the results. Caution should also be used
when interpreting results based on a relatively small number of cases. Summary measures
(such as medians and percentage distributions) probably do not reveal useful information
when computed on a subpopulation smaller than 75,000.
For additional information on nonsampling error, including the possible impact on CPS
data, when known, refer to U.S. Census Bureau (2019e) and Brooks & Bailar (1978).

Estimation of Median Incomes. The Census Bureau has changed the methodology for
computing median income over time. The Census Bureau has computed medians using
either Pareto interpolation or linear interpolation. Currently, we are using linear
interpolation to estimate all medians. Pareto interpolation assumes a decreasing density of
population within an income interval, whereas linear interpolation assumes a constant
density of population within an income interval.
The Census Bureau calculated estimates of median income and associated standard errors
for 1979 through 1987 using Pareto interpolation if the estimate was larger than $20,000
for people or $40,000 for families and households. We calculated estimates of median
income and associated standard errors for 1976, 1977, and 1978 using Pareto
interpolation if the estimate was larger than $12,000 for people or $18,000 for families and
households. All other estimates of median income and associated standard errors for 1976
through 2019 (2020 CPS ASEC), and almost all of the estimates of median income and
associated standard errors for 1975 and earlier, were calculated using linear interpolation.
Thus, use caution when comparing median incomes above $12,000 for people or $18,000
15

The phase-in process using the 2010 Census files began April 2014.

G-12

SOURCE & ACCURACY

for families and households for different years. Median incomes below those levels are
more comparable from year to year since they have always been calculated using linear
interpolation. For an indication of the comparability of medians calculated using Pareto
interpolation with medians calculated using linear interpolation, see U.S. Census Bureau
(1978) and U.S. Census Bureau (1993).

Standard Errors and Their Use. A sample estimate and its standard error enable one to
construct a confidence interval. A confidence interval is a range about a given estimate that
has a specified probability of containing the average result of all possible samples. For
example, if all possible samples were surveyed under essentially the same general
conditions and using the same sample design, and if an estimate and its standard error
were calculated from each sample, then approximately 90 percent of the intervals from
1.645 standard errors below the estimate to 1.645 standard errors above the estimate
would include the average result of all possible samples.
A particular confidence interval may or may not contain the average estimate derived from
all possible samples, but one can say with the specified confidence that the interval
includes the average estimate calculated from all possible samples.
Standard errors may also be used to perform hypothesis testing, a procedure for
distinguishing between population parameters using sample estimates. The most common
type of hypothesis is that the population parameters are different. An example of this
would be comparing the percentage of men who were part-time workers to the percentage
of women who were part-time workers.

Tests may be performed at various levels of significance. A significance level is the
probability of concluding that the characteristics are different when, in fact, they are the
same. For example, to conclude that two characteristics are different at the 0.10 level of
significance, the absolute value of the estimated difference between characteristics must be
greater than or equal to 1.645 times the standard error of the difference.

The Census Bureau uses 90-percent confidence intervals and 0.10 levels of significance to
determine statistical validity. Consult standard statistical textbooks for alternative criteria.

The tables in Income and Poverty in the United States: 2019, Health Insurance Coverage in
the United States: 2019, and The Supplemental Poverty Measure: 2019 list estimates
followed by a number labeled “Margin of Error (±).” This number can be added to and
subtracted from the estimates to calculate upper and lower bounds of the 90-percent
confidence interval. For example, Health Insurance Coverage in the United States: 2019
shows the numbers for health insurance. For the statement, “8.0 percent of people were
uninsured for the entire calendar year,” the 90-percent confidence interval for the estimate,
8.0 percent, is 8.0 (± 0.2) percent, or 7.8 percent to 8.2 percent. 16
16

Note that the confidence interval here does not match the confidence interval given in Illustration 3
because the standard errors/margin of errors were calculated in two different ways. The margin of
errors within the tables in the reports are calculated using direct estimates, whereas the standard errors
within the illustrations later in this document are calculated using generalized variance estimates.

SOURCE & ACCURACY

G-13

Estimating Standard Errors. The Census Bureau uses replication methods to estimate the
standard errors of CPS and ASEC estimates. These methods primarily measure the
magnitude of sampling error. However, they do measure some effects of nonsampling
error as well. They do not measure systematic biases in the data associated with
nonsampling error. Bias is the average over all possible samples of the differences between
the sample estimates and the true value.
There are two ways to calculate standard errors for the 2020 CPS ASEC microdata file.
1. Direct estimates created from replicate weighting methods;
2. Generalized variance estimates created from generalized variance function
(GVF) parameters a and b.

While replicate weighting methods provide the most accurate variance estimates, this
approach requires more computing resources and more expertise on the part of the user.
The GVF parameters provide a method of balancing accuracy with resource usage as well
as a smoothing effect on standard error estimates. For more information on calculating
direct estimates, refer to the “Replicate Weighting” section. For more information on GVF
estimates, refer to the “Generalized Variance Parameters” section.

The Income and Poverty in the United States: 2019, Health Insurance Coverage in the United
States: 2019, and The Supplemental Poverty Measure: 2019 reports use replicate weights to
calculate the margins of error of the estimates seen in tables and throughout the reports.
In 2009, the Census Bureau released replicate weights for the 2005 through 2009 CPS ASEC
collection years and has released replicate weights for each year since with the release of
the CPS ASEC public use data. Since the published GVF parameters generally
underestimated standard errors, standard errors produced using direct estimates may be
higher than in previous reports. For most CPS ASEC estimates, the increase in standard
errors from GVF to direct estimates will not alter the findings. However, marginally
significant differences using the GVF may not be significant using replicate weights.
The examples in this source and accuracy statement are for guidance calculating standard
errors using the generalized variance parameters. The use of generalized variance
parameters is the recommended method of calculating standard errors for data users who
do not have the ability to calculate the standard errors using replicate weights.
Replicate Weighting. The Census Bureau is releasing public use replicate weight files for
the 2020 CPS ASEC that can be matched to the microdata files.

Replicate estimates are created using each of the 160 weights independently to create 160
replicate estimates. For point estimates, multiply the replicate weights by the item of
interest at the record level (either an indicator variable to determine the number of people
with a characteristic or a variable that contains some value) and tally the weighted values
to create the 160 replicate estimates. Use these replicate estimates in formula (1) below to
G-14

SOURCE & ACCURACY

calculate the total variance for the item of interest. For example, say that the item of
interest is the number of males. Tally the weights for all the records that indicated male to
create the 160 replicate estimates of the number of males. Then use these estimates in the
formula to calculate the total variance for the number of males.
Calculate variance estimates for the estimates using:
var�𝜃𝜃�0 � =

4

160

� 2
�
∑160
𝑖𝑖=1 �𝜃𝜃𝑖𝑖 − 𝜃𝜃0 �

(1)

where 𝜃𝜃�0 is the estimate of the statistic of interest, such as a point estimate or proportion,
using the weight for the full sample, and 𝜃𝜃�𝑖𝑖 are the replicate estimates of the same statistic
using the replicate weights. The standard error is the square root of the variance.
For more information on using replicate weights and calculating direct estimates, see U.S.
Census Bureau (2009).

Generalized Variance Parameters. While it is possible to estimate the standard error
based on the survey data for each estimate in a report, there are a number of reasons why
this is not done. A presentation of the individual standard errors would be of limited use,
since one could not possibly predict all of the combinations of results that may be of
interest to data users. Additionally, data users have access to CPS microdata files, and it is
impossible to compute in advance the standard error for every estimate one might obtain
from those data sets. Moreover, variance estimates are based on sample data and have
variances of their own. Therefore, some methods of stabilizing these estimates of variance,
for example, by generalizing or averaging over time, may be used to improve their
reliability.
Experience has shown that certain groups of estimates have similar relationships between
their variances and expected values. Modeling or generalizing may provide more stable
variance estimates by taking advantage of these similarities. The GVF is a simple model
that expresses the variance as a function of the expected value of the survey estimate. The
parameters of the GVF are estimated using direct replicate variances. These GVF
parameters provide a relatively easy method to obtain approximate standard errors for
numerous characteristics.
In this source and accuracy statement:
•
•
•
•
•
•

Tables 4 through 17 provide illustrations for calculating standard errors;
Table 18 provides the GVF parameters for labor force estimates;
Table 19 provides GVF parameters for characteristics from the 2020 CPS ASEC;
Tables 20 and 21 provide correlation coefficients for comparing estimates from
consecutive years;
Table 22 provides correlation coefficients between race and subgroups; and
Tables 23 and 24 provide factors and population controls to derive state and
regional parameters.

SOURCE & ACCURACY

G-15

The basic CPS questionnaire records the race and ethnicity of each respondent. With
respect to race, a respondent can be White, Black, Asian, American Indian and Alaskan
Native (AIAN), Native Hawaiian and Other Pacific Islander (NHOPI), or combinations of two
or more of the preceding. A respondent’s ethnicity can be Hispanic or non-Hispanic,
regardless of race.
The GVF parameters to use in computing standard errors are dependent upon the
race/ethnicity group of interest. Table 3 summarizes the relationship between the
race/ethnicity group of interest and the GVF parameters to use in standard error
calculations.

G-16

SOURCE & ACCURACY

Table 3. Estimation Groups of Interest and Generalized Variance Parameters
Generalized variance parameters to
Race/ethnicity group of interest
use in standard error calculations
Total population

White alone, White alone or in combination (AOIC), or
White non-Hispanic population

Black alone, Black AOIC, or Black non-Hispanic population

Asian alone, Asian AOIC, or Asian non-Hispanic population
AIAN alone, AIAN AOIC, or AIAN non-Hispanic population
NHOPI alone, NHOPI AOIC, or NHOPI non-Hispanic
population
Populations from other race groups
HispanicA population

Two or more racesB – employment/unemployment and
educational attainment characteristics
Two or more racesB – all other characteristics

Total or White
Total or White
Black

Asian, American Indian and Alaska
Native (AIAN), Native Hawaiian and
Other Pacific Islander (NHOPI)
Asian, AIAN, NHOPI
Asian, AIAN, NHOPI
Asian, AIAN, NHOPI
HispanicA
Black

Asian, AIAN, NHOPI

Source: U.S. Census Bureau, Current Population Survey, internal data files.
A
Hispanics may be any race.
B
Two or more races refers to the group of cases self-classified as having two or more races.
Note: The AOIC population for a race group of interest includes people reporting only the race group of
interest (alone) and people reporting multiple race categories including the race group of interest (in
combination).

When calculating standard errors for an estimate of interest from cross-tabulations
involving different characteristics, use the set of GVF parameters for the characteristic that
will give the largest standard error. If the estimate of interest is strictly from basic CPS
data, the GVF parameters will come from the CPS GVF table (Table 18). If the estimate is
using ASEC data, the GVF parameters will come from the ASEC GVF table (Table 19).
Standard Errors of Estimated Numbers. The approximate standard error, 𝑠𝑠𝑥𝑥 , of an
estimated number from this microdata file can be obtained by using the formula:
𝑠𝑠𝑥𝑥 = √𝑎𝑎𝑥𝑥 2 + 𝑏𝑏𝑏𝑏

Here x is the size of the estimate, and a and b are the parameters in Table 18 or 19
associated with the particular type of characteristic.

SOURCE & ACCURACY

(2)

G-17

Illustration 1
Suppose there were 3,826,000 unemployed females (ages 16 and up) in the civilian labor
force. Table 4 shows how to use the appropriate parameters from Table 18 and Formula
(2) to estimate the standard error and confidence interval.
Table 4. Illustration of Standard Errors of Estimated Numbers
Number of unemployed females in the civilian labor force (x)
3,826,000
a-parameter (a)
-0.000028
b-parameter (b)
2,788
Standard error
101,000
90-percent confidence interval
3,660,000 to 3,992,000

Source: U.S. Census Bureau, Current Population Survey, March 2020.

The standard error is calculated as

𝑠𝑠𝑥𝑥 = �−0.000028 × 3,826,0002 + 2,788 × 3,826,000,

which, rounded to the nearest thousand, is 101,000. The 90-percent confidence interval is
calculated as 3,826,000 ± 1.645 × 101,000.
A conclusion that the average estimate derived from all possible samples lies within a
range computed in this way would be correct for roughly 90 percent of all possible
samples.

Illustration 2
Suppose there were 62,342,000 married-couple family households. Table 5 shows how to
use the appropriate parameters from Table 19 and Formula (2) to estimate the standard
error and confidence interval.
Table 5. Second Illustration of Standard Errors of Estimated Numbers
Number of married-couple family households (x)
62,342,000
a-parameter (a)
-0.000009
b-parameter (b)
3,238
Standard error
409,000
90-percent confidence interval
61,669,000 to 63,015,000

Source: U.S. Census Bureau, Current Population Survey, 2020 Annual Social and Economic Supplement.

The standard error is calculated as

𝑠𝑠𝑥𝑥 = �−0.000009 × 62,342,0002 + 3,238 × 62,342,000

which, rounded to the nearest thousand, is 409,000. The 90-percent confidence interval is
calculated as 62,342,000 ± 1.645 × 409,000.
G-18

SOURCE & ACCURACY

A conclusion that the average estimate derived from all possible samples lies within a
range computed in this way would be correct for roughly 90 percent of all possible
samples.

Standard Errors of Estimated Percentages. The reliability of an estimated percentage,
computed using sample data for both numerator and denominator, depends on both the
size of the percentage and its base. Estimated percentages are relatively more reliable than
the corresponding estimates of the numerators of the percentages, particularly if the
percentages are 50 percent or more. When the numerator and denominator of the
percentage are in different categories, use the parameter from Table 18 or 19 as indicated
by the numerator.
The approximate standard error, 𝑠𝑠𝑦𝑦,𝑝𝑝 , of an estimated percentage can be obtained by using
the formula:
𝑏𝑏

𝑠𝑠𝑦𝑦,𝑝𝑝 = � 𝑝𝑝(100 − 𝑝𝑝)
𝑦𝑦

(3)

Here y is the total number of people, families, households, or unrelated individuals in the
base or denominator of the percentage, p is the percentage 100*x/y (0 ≤ p ≤ 100), and b is
the parameter in Table 18 or 19 associated with the characteristic in the numerator of the
percentage.

Illustration 3
The report, Health Insurance Coverage in the United States: 2019, shows that there were
26,111,000 out of 324,550,000 people, or 8.0 percent, who did not have health insurance.
Table 6 shows how to use the appropriate parameters from Table 19 and Formula (3) to
estimate the standard error and confidence interval.
Table 6. Illustration of Standard Errors of Estimated Percentages
8.0
Percentage of people without health insurance (p)
Base (y)
324,550,000
b-parameter (b)
3,022
Standard error
0.08
90-percent confidence interval
7.9 to 8.1

Source: U.S. Census Bureau, Current Population Survey, 2020 Annual Social and Economic Supplement.

The standard error is calculated as

3,022
𝑠𝑠𝑦𝑦,𝑝𝑝 = �
× 8.0 × (100.0 − 8.0) = 0.08
324,550,000

and the 90-percent confidence interval for the estimated percentage of people without
health insurance is from 7.9 to 8.1 percent (i.e., 8.0 ± 1.645 × 0.08).
SOURCE & ACCURACY

G-19

Standard Errors of Estimated Differences. The standard error of the difference between
two sample estimates is approximately equal to
𝑠𝑠𝑥𝑥1 −𝑥𝑥2 = �𝑠𝑠𝑥𝑥1 2 + 𝑠𝑠𝑥𝑥2 2 − 2𝑟𝑟𝑠𝑠𝑥𝑥1 𝑠𝑠𝑥𝑥2

(4)

where 𝑠𝑠𝑥𝑥1 and 𝑠𝑠𝑥𝑥2 are the standard errors of the estimates, 𝑥𝑥1 and 𝑥𝑥2 . The estimates can be
numbers, percentages, ratios, etc. Tables 20 and 21 contain the correlation coefficient, r,
for CPS year-to-year comparisons for CPS poverty, income, and health insurance estimates
of numbers and proportions. Table 22 contains the correlation coefficient r for making
comparisons between race categories that are subsets of one another. For example, to
compare the number of people in poverty who listed White as their only race to the
number of people in poverty who are White alone or in combination with another race, a
correlation coefficient is needed to account for the large overlap between the two groups.
For making other comparisons (including race overlapping where one group is not a
complete subset of the other), assume that r equals zero. Making this assumption will
result in accurate estimates of standard errors for the difference between two estimates of
the same characteristic in two different areas, or for the difference between separate and
uncorrelated characteristics in the same area. However, if there is a high positive
(negative) correlation between the two characteristics, the formula will overestimate
(underestimate) the true standard error.

Illustration 4
Suppose there were 25,886,000 men over age 24 who were never married and 10,626,000
men over age 24 who were divorced. The apparent difference is 15,260,000. Table 7
shows how to use Formulas (2) and (4) with r = 0 and the appropriate parameters from
Table 19 to estimate the standard errors and confidence intervals.
Table 7. Illustration of Standard Errors of Estimated Differences
Difference
Never married (x1)
Divorced (x2)
Number of males over age 24
25,886,000
10,626,000
15,260,000
a-parameter (a)
-0.000009
-0.000009
b-parameter (b)
2,808
2,808
Standard error
258,000
170,000
309,000
90-percent confidence
25,462,000 to
10,346,000 to
14,752,000 to
interval
26,310,000
10,906,000
15,768,000

Source: U.S. Census Bureau, Current Population Survey, 2020 Annual Social and Economic Supplement.

The standard error of the difference is calculated as

𝑠𝑠𝑥𝑥1 −𝑥𝑥2 = �258,0002 + 170,0002

which, rounded to the nearest thousand, is 309,000. The 90-percent confidence interval
around the difference is calculated as 15,260,000 ± 1.645 × 309,000. Since this interval
G-20

SOURCE & ACCURACY

does not include zero, we can conclude with 90-percent confidence that the number of
never-married men over age 24 was higher than the number of divorced men over age 24.
Illustration 5
The report, Income and Poverty in the United States: 2019, shows that 11,869,000 out of
73,284,000 children, or 16.2 percent, were reported as in poverty in 2018, and that
10,466,000 out of 72,637,000, or 14.4 percent, were in poverty in 2019. The apparent
difference is 1.8 percent. Table 8 shows how to use the appropriate parameters from Table
19 and Formulas (3) and (4) to estimate the standard error and confidence interval.
Table 8. Illustration of Standard Errors of Estimated Differences
Difference
2018 (x1)
2019 (x2)
16.2
14.4
1.8
Percentage of children in poverty (p)
Base
73,284,000
72,637,000
b-parameter (b)
2,718A
3,781
Correlation coefficient (r)
0.45
Standard error
0.22
0.25
0.25
90-percent confidence interval
15.8 to 16.6
14.0 to 14.8
1.4 to 2.2

Source: U.S. Census Bureau, Current Population Survey, 2019-2020 Annual Social and Economic Supplement.
A This value comes from the Source and Accuracy Statement for the 2019 Annual Social and Economic
Supplement, Appendix G, Table 19 in U.S. Census Bureau (2019d). For additional information, see the
“Year-to-Year Factors” section.

The standard error of the difference is calculated as

𝑠𝑠𝑥𝑥1 −𝑥𝑥2 = �0.222 + 0.252 − 2 × 0.45 × 0.22 × 0.25 = 0.25

and the 90-percent confidence interval around the difference is calculated as 1.8 ± 1.645 ×
0.25. Since this interval does not include zero, we can conclude with 90-percent confidence
that the percentage of children in poverty in 2019 is significantly less than the percentage
of children in poverty in 2018.
Standard Errors of Estimated Ratios. Certain estimates may be calculated as the ratio of
two numbers. Compute the standard error of a ratio, x/y, using
2

𝑠𝑠

2

𝑥𝑥
𝑠𝑠
𝑦𝑦
𝑠𝑠𝑥𝑥⁄𝑦𝑦 = �� 𝑥𝑥� + � � − 2𝑟𝑟
𝑦𝑦

𝑥𝑥

𝑦𝑦

𝑠𝑠𝑥𝑥 𝑠𝑠𝑦𝑦
𝑥𝑥𝑥𝑥

(5)

The standard error of the numerator, sx, and that of the denominator, sy, may be calculated
using formulas described earlier. In Formula (5), r represents the correlation between the
numerator and the denominator of the estimate.

For one type of ratio, the denominator is a count of families or households and the
numerator is a count of people in those families or households with a certain characteristic.
If there is at least one person with the characteristic in every family or household, use 0.7
as an estimate of r. An example of this type is the average number of children per family
with children.
SOURCE & ACCURACY

G-21

For all other types of ratios, r is assumed to be zero. Examples are the average number of
children per family and the family poverty rate. If r is actually positive (negative), then this
procedure will provide an overestimate (underestimate) of the standard error of the ratio.
Note: For estimates expressed as the ratio of x per 100 y or x per 1,000 y, multiply
Formula (5) by 100 or 1,000, respectively, to obtain the standard error.

Illustration 6
Suppose there were 11,328,000 males working part-time and 17,534,000 females working
part-time. The ratio of males working part-time to females working part-time would be
0.646, or 64.6 percent. Table 9 shows how to use the appropriate parameters from Table
18 and Formulas (2) and (5) with r = 0 to estimate the standard errors and confidence
intervals.

Table 9. Illustration of Standard Errors of Estimated Ratios
Males (x)
Females (y)
Number who work part-time
11,328,000
17,534,000
a-parameter (a)
-0.000031
-0.000028
b-parameter (b)
2,947
2,788
Standard error
171,000
201,000
90-percent confidence interval 11,047,000 to 11,609,000 17,203,000 to 17,865,000
Source: U.S. Census Bureau, Current Population Survey, March 2020.

The standard error is calculated as
𝑠𝑠𝑥𝑥⁄𝑦𝑦 =

Ratio
0.646
0.012
0.626 to 0.666

11,328,000
171,000 2
201,000 2
��
� +�
� = 0.012
17,534,000 11,328,000
17,534,000

and the 90-percent confidence interval is calculated as 0.646 ± 1.645 × 0.012.

Illustration 7
The report, Income and Poverty in the United States: 2019, shows that the number of
families below the poverty level, 𝑥𝑥, was 6,554,000 and the total number of families, 𝑦𝑦, was
83,698,000. The ratio of families below the poverty level to the total number of families
would be 0.078 or 7.8 percent. Table 10 shows how to use the appropriate parameters
from Table 19 and Formulas (2) and (5) with r = 0 to estimate the standard errors and
confidence intervals.

G-22

SOURCE & ACCURACY

Table 10. Second Illustration of Standard Errors of Estimated Ratios
In poverty (x)
Total (y)
Ratio (in percent)
Number of families
6,554,000
83,698,000
7.8
a-parameter (a)
0.000103
-0.000009
b-parameter (b)
5,529
3,238
Standard error
202,000
456,000
0.24
90-percent confidence interval
6,222,000 to 6,886,000 82,948,000 to 84,448,000
7.4 to 8.2
Source: U.S. Census Bureau, Current Population Survey, 2020 Annual Social and Economic Supplement.

The standard error is calculated as
𝑠𝑠𝑥𝑥⁄𝑦𝑦 =

202,000 2
6,554,000
456,000 2
��
� +�
� = 0.0024 = 0.24%
83,698,000 6,554,000
83,698,000

and the 90-percent confidence interval of the percentage is calculated as 7.8 ± 1.645 × 0.24.
Standard Errors of Estimated Medians. The sampling variability of an estimated median
depends on the form of the distribution and the size of the base. One can approximate the
reliability of an estimated median by determining a confidence interval about it. (See
“Standard Errors and Their Use” for a general discussion of confidence intervals.)

Estimate the 68-percent confidence limits of a median based on sample data using the
following procedure:
1.
2.
3.

Using Formula (3) and the base of the distribution, calculate the standard error of
50 percent.

Add to and subtract from 50 percent the standard error determined in step 1. These
two numbers are the percentage limits corresponding to the 68-percent confidence
interval about the estimated median.
Using the distribution of the characteristic, determine upper and lower limits of the
68-percent confidence interval by calculating values corresponding to the two
points established in step 2.
Note: The percentage limits found in step 2 may or may not fall in the same
characteristic distribution interval.
Use the following formula to calculate the upper and lower limits:
where

SOURCE & ACCURACY

𝑋𝑋𝑝𝑝 =

𝑝𝑝𝑝𝑝−𝑁𝑁1
𝑁𝑁2 −𝑁𝑁1

(𝐴𝐴2 − 𝐴𝐴1 ) + 𝐴𝐴1

(6)

G-23

Xp

=

N

=

p

=

A1, A2

=

N1, N2

=
=
=

4.

estimated upper and lower bounds for the confidence interval
(0 ≤ p ≤ 1). For purposes of calculating the confidence interval,
p takes on the values determined in step 2. Note that Xp
estimates the median when p = 0.50.
for distribution of numbers: the total number of units (people,
households, etc.) for the characteristic in the distribution.
for distribution of percentages: the value 100.
the values obtained in Step 2.

the lower and upper bounds, respectively, of the interval
containing Xp.

for distribution of numbers: the estimated number of units
(people, households, etc.) with values of the characteristic less
than or equal to A1 and A2, respectively.
for distribution of percentages: the estimated percentage of
units (people, households, etc.) having values of the
characteristic less than or equal to A1 and A2, respectively.

Divide the difference between the two points determined in step 3 by 2 to obtain the
standard error of the median.

Note: Median incomes and their standard errors calculated as below may differ from
those in published tables and reports showing income, since narrower income
intervals were used in those calculations.
Illustration 8
The report, Income and Poverty in the United States: 2019, shows that there were
128,451,000 households, and their income was distributed as shown in Table 11.

G-24

SOURCE & ACCURACY

Table 11. Distribution of Household Income for Illustration 8
Number of
Cumulative number of
Cumulative percent
Income level
households
households
of households
Under $5,000
3,821,000
3,821,000
2.97%
$5,000 to $9,999
2,833,000
6,654,000
5.18%
$10,000 to $14,999
5,003,000
11,657,000
9.08%
$15,000 to $24,999
10,287,000
21,944,000
17.08%
$25,000 to $34,999
10,828,000
32,772,000
25.51%
$35,000 to $49,999
14,980,000
47,752,000
37.18%
$50,000 to $74,999
21,057,000
68,809,000
53.57%
$75,000 to $99,999
15,923,000
84,732,000
65.96%
$100,000 and over
43,719,000
128,451,000*
100.00%*

Source: U.S. Census Bureau, Current Population Survey, 2020 Annual Social and Economic Supplement.
*There may be a difference due to rounding.

1.
2.
3.

Using Formula (3) with b = 3,938, the standard error of 50 percent on a base of
128,451,000 is about 0.28 percent.

To obtain a 68-percent confidence interval on an estimated median, add to and
subtract from 50 percent the standard error found in step 1. This yields percentage
limits of 49.72 and 50.28.

The lower and upper limits for the interval in which the percentage limits falls are
$50,000 and $75,000, respectively.
Then the estimated numbers of households with an income less than or equal to
$50,000 and $75,000 are 47,752,000 and 68,809,000, respectively.

Using Formula (6), the lower limit for the confidence interval of the median is found
to be about

𝑋𝑋0.4972 =

0.4972 × 128,451,000 − 47,752,000
(75,000 − 50,000) + 50,000 = 69,131
68,809,000 − 47,752,000

𝑋𝑋0.5028 =

0.5028 × 128,451,000 − 47,752,000
(75,000 − 50,000) + 50,000 = 69,985
68,809,000 − 47,752,000

Similarly, the upper limit is found to be about

4.

Thus, a 68-percent confidence interval for the median income for households is
from $69,131 to $69,985.
The standard error of the median is, therefore,

SOURCE & ACCURACY

69,985 − 69,131
= 427.0
2

G-25

Standard Errors of Averages for Grouped Data. The formula used to estimate the
standard error of an average for grouped data is
𝑏𝑏

𝑠𝑠𝑥𝑥̅ = � (𝑆𝑆 2 )

(7)

𝑆𝑆 2 = ∑𝑐𝑐𝑖𝑖=1 𝑝𝑝𝑖𝑖 𝑥𝑥̅𝑖𝑖2 − 𝑥𝑥̅ 2

(8)

𝑥𝑥̅ = ∑𝑐𝑐𝑖𝑖=1 𝑝𝑝𝑖𝑖 𝑥𝑥̅𝑖𝑖

(9)

𝑦𝑦

In this formula, y is the size of the base of the distribution and b is the parameter from
Table 4 or 5. The variance, S², is given by the following formula:
where x , the average of the distribution, is estimated by
where

c =
pi =

the number of groups; i indicates a specific group, thus taking on values 1
through c.

estimated proportion of households, families, or people whose values for the
characteristic being considered fall in group i.

xi = (ZLi + ZUi)/2 where ZLi and ZUi are the lower and upper interval boundaries,
respectively, for group i. xi is assumed to be the most representative value
for the characteristic of households, families, or people in group i. If group c
is open-ended, i.e., no upper interval boundary exists, use a group
approximate average value of
3

𝑥𝑥̅𝑐𝑐 = 𝑍𝑍𝐿𝐿𝑐𝑐
2

(10)

Illustration 9
The report, Income and Poverty in the United States: 2019, shows that there were 6,554,000
families in poverty. Table 12 shows the distribution of the income deficit (the difference
between their family income and poverty threshold) for all families in poverty.

G-26

SOURCE & ACCURACY

Table 12. Distribution of Income Deficit for Illustration 9
Number of
Average income
Percentage of families
families in
deficit ( xi )
in poverty (pi)
Income deficit
poverty
Under $1000
468,000
7.1%
500
$1000 to $2,499
514,000
7.8%
1,750
$2,500 to $4,999
899,000
13.7%
3,750
$5,000 to $7,499
805,000
12.3%
6,250
$7,500 to $9,999
760,000
11.6%
8,750
$10,000 to $12,499
589,000
9.0%
11,250
$12,500 to $14,999
528,000
8.1%
13,750
$15,000 and over
1,991,000
30.4%
22,500
Total
6,554,000*
100%*

Source: U.S. Census Bureau, Current Population Survey, 2020 Annual Social and Economic Supplement.
*There may be a difference due to rounding.

Using Formula (9),

𝑥𝑥̅ = (0.071 × 500) + (0.078 × 1,750) + (0.137 × 3,750) + (0.123 × 6,250) + (0.116 × 8,750)
+ (0.090 × 11,250) + (0.081 × 13,750) + (0.304 × 22,500) = 11,436

and Formula (8),

𝑆𝑆 2 = (0.071 × 5002 ) + (0.078 × 1,7502 ) + (0.137 × 3,7502 ) + (0.123 × 6,2502 )
+ (0.116 × 8,7502 ) + (0.090 × 11,2502 ) + (0.081 × 13,7502 ) + (0.304 × 22,5002 )
− 11,4362 = 65,692,000

Table 13 shows how to use the appropriate parameter from Table 19 and Formula (7) to
estimate the standard error and confidence interval.
Table 13. Illustration of Standard Errors of Averages for Grouped Data
Average income deficit for families in poverty (x )
$11,436
Variance (S2)
65,692,000
Base (y)
6,554,000
b-parameter (b)
5,529
Standard error
$235
90-percent confidence interval
$11,049 to $11,823

Source: U.S. Census Bureau, Current Population Survey, 2020 Annual Social and Economic Supplement.

The standard error is calculated as

5,529
(65,692,000) = 235
𝑠𝑠𝑥𝑥̅ = �
6,554,000

and the 90-percent confidence interval is calculated as $11,436 ± 1.645 × $235.
SOURCE & ACCURACY

G-27

Standard Errors of Estimated Per Capita Deficits. Certain average values in reports
associated with the CPS ASEC data represent the per capita deficit for households of a
certain class. The average per capita deficit is approximately equal to
where

𝑥𝑥 =

ℎ𝑚𝑚
𝑝𝑝

h =

number of households in the class.

p =

number of people in households in the class.

m=
x =

(11)

average deficit for households in the class.

average per capita deficit of people in households in the class.

To approximate standard errors for these averages, use the formula
𝑠𝑠𝑥𝑥 =

ℎ𝑚𝑚
𝑝𝑝

2

𝑠𝑠

2

2

𝑠𝑠

��𝑠𝑠𝑚𝑚 � + � 𝑝𝑝 � + �𝑠𝑠ℎ� − 2𝑟𝑟 � 𝑝𝑝 � �𝑠𝑠ℎ�
𝑚𝑚

𝑝𝑝

ℎ

𝑝𝑝

In Formula (12), r represents the correlation between p and h.

ℎ

(12)

For one type of average, the class represents households containing a fixed number of
people. For example, h could be the number of 3-person households. In this case, there is
an exact correlation between the number of people in households and the number of
households. Therefore, r = 1 for such households. For other types of averages, the class
represents households of other demographic types, for example, households in distinct
regions, households in which the householder is of a certain age group, and owneroccupied and tenant-occupied households. In this and other cases in which the correlation
between p and h is not perfect, use 0.7 as an estimate of r.
Illustration 10
The report, Income and Poverty in the United States: 2019, shows that there were
22,431,000 people living in families in poverty, and 6,554,000 families in poverty, with an
average deficit income for families in poverty of $11,436 with a standard error of $235
(from Illustration 9). Table 14 shows how to use Formulas (2), (11), and (12) and the
appropriate parameters from Table 19 and r = 0.7 to estimate the standard errors and
confidence intervals.

G-28

SOURCE & ACCURACY

Table 14. Illustration of Standard Errors of Estimated Medians
Number of
Average income
Average per
Number (h)
people (p)
deficit (m)
capita deficit (x)
Value for families in
poverty
6,554,000
22,431,000
$11,436
$3,341
a-parameter (a)
0.000103
-0.000113
b-parameter (b)
5,529
3,838
Correlation (r)
0.7
Standard error
202,000
171,000
$235
$111
90-percent
6,222,000 to
22,150,000 to
$11,049 to
$3,158 to
confidence interval
6,886,000
22,712,000
$11,823
$3,524

Source: U.S. Census Bureau, Current Population Survey, 2020 Annual Social and Economic Supplement.

The estimate of the average per capita deficit is calculated as
𝑥𝑥 =

6,554,000 × 11,436
= 3,341
22,431,000

and the standard error is calculated as
𝑠𝑠𝑥𝑥 =

6,554,000 × 11,436
171,000 2
202,000 2
171,000
202,000
235 2
��
� +�
� +�
� − 2 × 0.7 × �
��
�
22,431,000
22,431,000
6,554,000
22,431,000
6,554,000
11,436

= 111

The 90-percent confidence interval is calculated as $3,341 ± 1.645 × $111.

Accuracy of State Estimates. The redesign of the CPS following the 1980 census provided
an opportunity to increase efficiency and accuracy of state data. All strata are now defined
within state boundaries. The sample is allocated among the states to produce state and
national estimates with the required accuracy while keeping total sample size to a
minimum. Improved accuracy of state data was achieved with about the same sample size
as in the 1970 design.

Since the CPS is designed to produce both state and national estimates, the proportion of
the total population sampled and the sampling rates differ among the states. In general, the
smaller the population of the state the larger the sampling proportion. For example, in
Vermont, approximately 1 in every 250 households is sampled each month. In New York,
the sample is about 1 in every 2,000 households. Nevertheless, the size of the sample in
New York is four times larger than in Vermont because New York has a larger population.
Note: The Census Bureau recommends the use of 3-year averages to compare estimates
across states and 2-year averages to evaluate changes in state income and poverty
estimates over time. See “Standard Errors of Data for Combined Years.” Further,
the Income and Poverty in the United States report no longer presents state
estimates. Therefore, the Census Bureau recommends the American Community
Survey (ACS) microdata file as the preferred source for income and poverty state
SOURCE & ACCURACY

G-29

data in years 2006 (2005 estimates) to the present. A questionnaire redesign
introduced with the 2014 CPS ASEC and an updated processing system introduced
with the 2019 CPS ASEC each mark the start of new time series for health insurance
estimates in the CPS ASEC, so data users should not create multiyear averages
across these years.

Standard Errors of State Estimates. The standard error for a state may be obtained by
determining new state-level a- and b-parameters and then using these adjusted parameters
in the standard error formulas mentioned previously. To determine a new state-level bparameter (bstate), multiply the b-parameter from Table 18 or 19 by the state factor from
Table 23. To determine a new state-level a-parameter (astate), use the following:
(1)
(2)

If the a-parameter from Table 18 or 19 is positive, multiply it by the state
factor from Table 23.

If the a-parameter in Table 18 or 19 is negative, calculate the new state-level
a-parameter as follows:
𝑎𝑎𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 =

−𝑏𝑏𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝑃𝑃𝑃𝑃𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

where POPstate is the state population found in Table 23.

(13)

Illustration 11
Suppose there were 14,201,000 people living in New York state who were born in the
United States. Table 15 shows how to use Formulas (2) and (13) and the appropriate
parameter, factor, and population from Tables 19 and 23 to estimate the standard error
and confidence interval.
Table 15. Illustration of Standard Errors of State Estimates
Number of people in New York born in the U.S. (x)
14,201,000
b-parameter (b)
2,808
New York state factor
1.19
State population
19,173,378
State b-parameter (bstate)
3,342
State a-parameter (astate)
-0.000174
Standard error
111,000
90-percent confidence interval
14,018,000 to 14,384,000

Source: U.S. Census Bureau, Current Population Survey, 2020 Annual Social and Economic Supplement.

Obtain the state-level b-parameter by multiplying the b-parameter, 2,808 by the state
factor, 1.19. This gives bstate = 2,808 × 1.19 = 3,342. Obtain the needed state-level aparameter by

G-30

𝑎𝑎𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 =

−3,342
= −0.000174
19,173,378

SOURCE & ACCURACY

The standard error of the estimate of the number of people in New York state who were
born in the United States can then be found by using Formula (2) and the new state-level aand b- parameters, -0.000174 and 3,342, respectively. The standard error is given by
𝑠𝑠𝑥𝑥 = �−0.000174 × 14,201,0002 + 3,342 × 14,201,000

which, rounded to the nearest thousand, is 111,000.

Standard Errors of Regional Estimates. To compute standard errors for regional
estimates, follow the steps for computing standard errors for state estimates found in
“Standard Errors for State Estimates” using the regional factors and populations found in
Table 24.

Illustration 12
The report, Income and Poverty in the United States: 2019, shows that there were
14,845,000 of 124,032,005 people, or 12.0 percent, living in poverty in the South. Table 16
shows how to use Formulas (3) and (13) and the appropriate parameter, factor, and
population from Tables 19 and 24 to estimate the standard error and confidence interval.
Table 16. Illustration of Standard Errors of Regional Estimates
Poverty rate in the South (p)
12.0
Base (y)
124,032,005
b-parameter (b)
3,838
South regional factor
1.13
Regional b-parameter (bregion)
4,337
Standard error
0.19
90-percent confidence interval
11.7 to 12.3

Source: U.S. Census Bureau, Current Population Survey, 2020 Annual Social and Economic Supplement.

Obtain the region-level b-parameter by multiplying the b-parameter, 3,838, by the South
regional factor, 1.13. This gives bregion = 3,838 × 1.13 = 4,337
The standard error of the estimate of the poverty rate for people living in the South can
then be found by using Formula (3) and the new region-level b-parameter, 4,337. The
standard error is given by
4,337
𝑠𝑠𝑦𝑦,𝑝𝑝 = �
× 12.0 × (100 − 12.0) = 0.19
124,032,005

and the 90-percent confidence interval of the poverty rate for people living in the South is
calculated as 12.0 ± 1.645 × 0.19.

Standard Errors of Groups of States. The standard error calculation for a group of states
is similar to the standard error calculation for a single state. First, calculate a new state
SOURCE & ACCURACY

G-31

group factor for the group of states. Then, determine new state group a- and b-parameters.
Finally, use these adjusted parameters in the standard error formulas mentioned
previously.
Use the following formula to determine a new state group factor:
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 =

∑𝑛𝑛
𝑖𝑖=1 𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 ×𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑖𝑖

(14)

∑𝑛𝑛
𝑖𝑖=1 𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖

where POPi and state factori are the population and factor for state i from Table 23. To
obtain a new state group b-parameter (bstate group), multiply the b-parameter from Table 18
or 19 by the state group factor obtained by Formula (14). To determine a new state group
a-parameter (astate group), use the following:
(1)
(2)

If the a-parameter from Table 18 or 19 is positive, multiply it by the state
group factor determined by Formula (14).

If the a-parameter in Table 18 or 19 is negative, calculate the new state group
a-parameter as follows:
𝑎𝑎𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 =

−𝑏𝑏𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔
∑𝑛𝑛
𝑖𝑖=1 𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖

(15)

Illustration 13
Suppose the state group factor for the state group Illinois-Indiana-Michigan was required.
The appropriate factor would be
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 =

12,451,406 × 1.17 + 6,657,419 × 1.11 + 9,883,888 × 1.11
= 1.14
12,451,406 + 6,657,419 + 9,883,888

Standard Errors of Data for Combined Years. Sometimes estimates for multiple years
are combined to improve precision. For example, suppose x is an average derived from n
n
x
consecutive years’ data, i.e., x = ∑ i , where the xi are the estimates for the individual
i =1 n
years. Use the formulas described previously to estimate the standard error, s xi , of each
year’s estimate. Then the standard error of x is
where

G-32

𝑠𝑠𝑥𝑥̅ =

𝑠𝑠𝑥𝑥
𝑛𝑛

𝑠𝑠𝑥𝑥 = �∑𝑛𝑛𝑖𝑖=1 𝑠𝑠𝑥𝑥2𝑖𝑖 + 2𝑟𝑟 ∑𝑛𝑛−1
𝑖𝑖=1 𝑠𝑠𝑥𝑥𝑖𝑖 𝑠𝑠𝑥𝑥𝑖𝑖+1

(16)
(17)
SOURCE & ACCURACY

and s xi are the standard errors of the estimates xi. Tables 20 and 21 contain the correlation

coefficients, r, for the correlation between consecutive years i and i+1. Correlation between
nonconsecutive years is zero. The correlations were derived for income, poverty, and
health insurance estimates, but they can be used for other types of estimates where the
year-to-year correlation between identical households is high.
The Census Bureau recommends the use of 3-year average estimates for certain small
population subgroups 17 (see also “Accuracy of State Estimates.”) Two-year moving
averages are recommended for these small population subgroups for comparisons across
adjacent years.

Illustration 14
The report, Income and Poverty in the United States: 2019, provides the percentages of
families in poverty. Suppose the 2017-2019 18 3-year average percentage of families with
female householder, no husband present, in poverty was 24.4. Suppose the percentages
and bases for 2017, 2018, and 2019 were 26.2, 24.9, and 22.2 percent and 15,305,000,
15,052,000, and 14,838,000 respectively. Table 17 shows how to use the appropriate
parameters and correlation coefficients from Tables 19 and 21 and Formulas (3), (16), and
(17) to estimate the standard error and confidence interval.
Table 17. Illustration of Standard Errors of Data for Combined Years
2017-2019
2017
2018
2019
Average
Percentage of families with female
householder, no husband
present, in poverty (p)
26.2
24.9
22.2
24.4
Base (y)
15,305,000
15,052,000
14,838,000
b-parameter (b)
1,518A
3,631B
5,529
Correlation (r)
0.35
Standard error
0.44
0.67
0.80
0.46
90-percent confidence interval
25.5 to 26.9
23.8 to 26.0
20.9 to 23.5
23.6 to 25.2

Source: U.S. Census Bureau, Current Population Survey, 2018-2020 Annual Social and Economic Supplement.
A This value comes from the Source and Accuracy Statement for the 2018 Annual Social and Economic
Supplement, Appendix G, Table 19 in U.S. Census Bureau (2018). For additional information, see the
“Year-to-Year Factors” section.
B This value comes from the Source and Accuracy Statement for the 2019 Annual Social and Economic
Supplement, Appendix G, Table 19 in U.S. Census Bureau (2019d). For additional information, see the
“Year-to-Year Factors” section.

17

18

Estimates of characteristics of the American Indian and Alaska Native (AIAN) and Native Hawaiian and
Other Pacific Islander (NHOPI) populations based on a single-year sample would be unreliable due to the
small size of the sample that can be drawn from either population. Accordingly, such estimates are based
on multiyear averages.
The estimates for data year 2017 come from the CPS ASEC 2018 Bridge Files, and the estimates for data
year 2018 come from the 2019 CPS ASEC Files.

SOURCE & ACCURACY

G-33

The standard error of the 3-year average is calculated as
where

𝑠𝑠𝑥𝑥̅ =

1.37
= 0.46
3

𝑠𝑠𝑥𝑥 = �0.442 + 0.672 + 0.802 + (2 × 0.35 × 0.44 × 0.67) + (2 × 0.35 × 0.67 × 0.80) = 1.37

The 90-percent confidence interval for the 3-year average percentage of families with a
female householder, no husband present, in poverty is 24.4 ± 1.645 × 0.46.
Standard Errors of Quarterly or Yearly Averages. For information on calculating
standard errors for labor force data from the CPS which involve quarterly or yearly
averages, please see Bureau of Labor Statistics (2006).

Year-to-Year Factors. In past years, the Census Bureau published a table of year factors
for the CPS ASEC Supplement in the Source and Accuracy Statement. User demand for
these factors has diminished with the introduction of replicate weights. Data users
producing estimates from prior years should consult the Source and Accuracy Statements
covering the years of their analysis to estimate standard errors.

Technical Assistance. If you require assistance or additional information, please contact
the Demographic Statistical Methods Division via e-mail at
[email protected].

G-34

SOURCE & ACCURACY

Table 18. Parameters for Computation of Standard Errors for Labor Force Characteristics:
March 2020
Characteristic
Total or White
Civilian labor force, employed
Not in labor force
Unemployed
Civilian labor force, employed, not in labor force, and unemployed
Men
Women
Both sexes, 16 to 19 years

Black
Civilian labor force, employed, not in labor force, and unemployed
Men
Women
Both sexes, 16 to 19 years
Asian, American Indian and Alaska Native (AIAN), Native
Hawaiian and Other Pacific Islander (NHOPI)
Civilian labor force, employed, not in labor force, and unemployed
Men
Women
Both sexes, 16 to 19 years
Hispanic, may be of any race
Civilian labor force, employed, not in labor force, and unemployed
Men
Women
Both sexes, 16 to 19 years

a

b

-0.000013
-0.000013
-0.000017

2,481
2,432
3,244

-0.000031
-0.000028
-0.000261

2,947
2,788
3,244

-0.000117
-0.000249
-0.000190
-0.001425

3,601
3,465
3,191
3,601

-0.000245
-0.000537
-0.000399
-0.004078

3,311
3,397
2,874
3,311

-0.000087
-0.000172
-0.000158
-0.000909

3,316
3,276
3,001
3,316

Source: U.S. Census Bureau, Internal Current Population Survey data files for the 2010 Design.
Notes: These parameters are to be applied to basic CPS monthly labor force estimates. The Total or White,
Black, and Asian, AIAN, NHOPI parameters are to be used for both alone and in combination race
group estimates. For same-sex households, multiply the a- and b-parameters by 1.3. For
nonmetropolitan characteristics, multiply the a- and b-parameters by 1.5. If the characteristic of
interest is total state population, not subtotaled by race or ethnicity, the a- and b-parameters are
zero. For foreign-born and noncitizen characteristics for Total and White, the a- and b-parameters
should be multiplied by 1.3. No adjustment is necessary for foreign-born and noncitizen
characteristics for Black, Hispanic, and Asian, AIAN, NHOPI parameters. For the groups self-classified
as having two or more races, use the Asian, AIAN, NHOPI parameters for all employment
characteristics.

SOURCE & ACCURACY

G-35

Table 19. Parameters for Computation of Standard Errors for People and Families: 2020
Annual Social and Economic Supplement
Characteristics

Total or White

Black

Asian, AIAN, &
NHOPIA
a
b

HispanicB

a
b
a
b
a
PEOPLE
Educational attainment
-0.000011 3,483 -0.000041 3,187 -0.000086 2,906 -0.000053
Employment
-0.000013 2,481 -0.000117 3,601 -0.000245 3,311 -0.000087
People by family income
-0.000019 6,000 -0.000075 5,781 -0.000142 4,820 -0.000089
Income characteristics
Total
-0.000089 3,020 -0.000035 2,650 -0.000076 2,557 -0.000042
Male
-0.000081 2,736 -0.000074 2,685 -0.000155 2,538 -0.000097
Female
-0.000016 2,637 -0.000057 2,305 -0.000146 2,557 -0.000080
Age
15 to 24
-0.000084 3,524 -0.000297 3,449 -0.000516 2,841 -0.000185
25 to 44
-0.000096 3,242 -0.000146 3,259 -0.000276 2,805 -0.000168
45 to 64
-0.000098 3,317 -0.000140 2,457 -0.000354 2,557 -0.000221
65 and over
-0.000061 3,270 -0.000249 2,193 -0.000741 2,686 -0.000487
Health insurance
-0.000009 3,022 -0.000034 2,598 -0.000095 3,223 -0.000060
Marital status, household and family
Some household members
-0.000009 2,808 -0.000042 3,221 -0.000069 2,343 -0.000049
All household members
-0.000008 2,730 -0.000033 2,528 -0.000069 2,318 -0.000039
Mobility (movers)
Educational attainment, labor force, Marital
-0.000013 4,135 -0.000054 4,181 -0.000104 3,505 -0.000063
status, household, family, and income
US, county, state, region, or metropolitan
-0.000018 5,986 -0.000066 5,104 -0.000137 4,629 -0.000095
statistical areas
Below poverty
Total
-0.000113 3,838 -0.000108 3,667 -0.000092 3,099 -0.000106
Male
-0.000115 3,877 -0.000243 3,978 -0.000168 2,756 -0.000244
Female
-0.000107 3,603 -0.000206 3,589 -0.000182 3,183 -0.000210
Age
Under 15
-0.000171 5,771 -0.000678 5,651 -0.000474 3,953 -0.000872
Under 18
-0.000112 3,781 -0.000420 4,341 -0.000310 3,202 -0.000435
15 and over
-0.000128 4,341 -0.000154 4,095 -0.000134 3,547 -0.000153
15 to 24
-0.000090 3,785 -0.000730 4,017 -0.000544 2,996 -0.000632
25 to 44
-0.000101 3,428 -0.000394 4,007 -0.000301 3,059 -0.000335
45 to 64
-0.000099 3,356 -0.000418 3,020 -0.000385 2,782 -0.000413
65 and over
-0.000063 3,395 -0.000714 2,588 -0.000909 3,294 -0.000701
Unemployment
-0.000017 3,244 -0.000117 3,601 -0.000245 3,311 -0.000087
FAMILIES, HOUSEHOLDS, OR UNRELATED INDIVIDUALS
Income
-0.000030 3,938 -0.000184 3,930 -0.000261 3,420 -0.000134
Marital status, household and family,
educational attainment, population by age/sex -0.000009 3,238 -0.000066 2,550 -0.000285 3,754 -0.000074
Poverty
0.000103 5,529 0.000516 5,568 0.003231 3,933 0.000478
Source: U.S. Census Bureau, Current Population Survey, Internal data from the 2020 Annual Social and Economic
Supplement.

G-36

SOURCE & ACCURACY

b
3,233
3,316
5,403
2,549
2,952
2,412
2,800
3,023
2,730
2,324
3,633
2,941
2,348
3,841
5,734
3,572
3,993
3,659
7,270
4,495
4,066
3,477
3,406
2,987
2,538
3,316
3,866

3,758
6,075

AIAN is American Indian and Alaska Native, and NHOPI is Native Hawaiian and Other Pacific Islander.
Hispanics may be any race.
Notes: These parameters are to be applied to the 2020 Annual Social and Economic Supplement data. The Total or
White, Black, and Asian, AIAN, NHOPI parameters are to be used for both alone and in combination race group
estimates. For same-sex households, multiply the a- and b-parameters by 1.3. For nonmetropolitan
characteristics, multiply the a- and b-parameters by 1.5. If the characteristic of interest is total state population,
not subtotaled by race or ethnicity, the a- and b-parameters are zero. For foreign-born and noncitizen
characteristics for Total and White, the a- and b-parameters should be multiplied by 1.3. No adjustment is
necessary for foreign-born and noncitizen characteristics for Black, Asian, AIAN, NHOPI, and Hispanic parameters.
For the group self-classified as having two or more races, use the Asian, AIAN, NHOPI parameters for all
characteristics except employment, unemployment, and educational attainment, in which case use Black
parameters. For a more detailed discussion on the use of parameters for race and ethnicity, please see the
“Generalized Variance Parameters” section.

A
B

Table 20. Current Population Survey Year-to-Year Correlation Coefficients for Income and Health
Insurance Characteristics: Data Years 1960 to 2019
1960-2000 (basic)
Characteristics or 2000 (expanded)-2019

Total
White
Black
Other
HispanicA

1999 (basic)2000 (expanded)

People

Families

People

Families

0.30
0.30
0.30
0.30
0.45

0.35
0.35
0.35
0.35
0.55

0.19
0.20
0.15
0.15
0.36

0.22
0.23
0.18
0.17
0.28

Source: U.S. Census Bureau, Current Population Survey, Internal data files.
A
Hispanics may be any race.
Notes: Correlation coefficients are not available for income data before 1960. These correlation coefficients
are for comparisons of consecutive years. For comparisons of nonconsecutive years, assume the
correlation is zero. For households and unrelated individuals, use the correlation coefficient for
families. For a more detailed discussion on the use of parameters for race and ethnicity, please see
the “Generalized Variance Parameters” section.

SOURCE & ACCURACY

G-37

Table 21. Current Population Survey Year-to-Year Correlation Coefficients for Poverty
Characteristics: Data Years 1970 to 2019
1972-83, 19841999 (basic)2000 (basic)
1983-1984
1971-1972
1970-1971
or
2000
2000
(expanded)
Characteristics
(expanded)-2019
People Families People Families People Families People Families People Families
Total
White
Black
Other
HispanicA

0.45
0.35
0.45
0.45
0.65

0.35
0.30
0.35
0.35
0.55

0.29
0.23
0.23
0.22
0.52

0.22
0.20
0.18
0.17
0.40

0.39
0.30
0.39
0.30
0.56

0.30
0.26
0.30
0.30
0.47

0.15
0.14
0.17
0.17
0.17

0.14
0.13
0.16
0.16
0.16

0.31
0.28
0.35
0.35
0.35

0.28
0.25
0.32
0.32
0.32

Source: U.S. Census Bureau, Current Population Survey, Internal data files.
A
Hispanics may be any race.
Notes: Correlation coefficients are not available for poverty data before 1970. These correlation coefficients
are for comparisons of consecutive years. For comparisons of nonconsecutive years, assume the
correlation is zero. For households and unrelated individuals, use the correlation coefficient for
families. For a more detailed discussion on the use of parameters for race and ethnicity, please see
the “Generalized Variance Parameters” section.

Table 22. Current Population Survey Correlation Coefficients Between Race and Subgroups:
2020 Annual Social and Economic Supplement
Race 1 (subgroup)

Race 2

White alone, not Hispanic ..........
White alone, not Hispanic ..........
Black alone ........................................
Asian alone........................................

White alone ........................................................................
White alone or in combination, not Hispanic .....
Black alone or in combination ...................................
Asian alone or in combination...................................

𝒓𝒓

0.82
0.98
0.95
0.92

Source: U.S. Census Bureau, Current Population Survey, Internal data files.
Notes: For a more detailed discussion on the use of parameters for race and ethnicity, please see the
“Generalized Variance Parameters” section.

G-38

SOURCE & ACCURACY

Table 23. Factors and Populations for State Standard Errors and Parameters: 2020 Annual
Social and Economic Supplement
State
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
District of Columbia
Florida
Georgia
Hawaii
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri

Factor

Population

State

1.11
0.18
1.25
0.73
1.28
1.22
0.86
0.22
0.17
1.14
1.15
0.32
0.41
1.17
1.11
0.77
0.82
1.13
1.01
0.39
1.15
1.10
1.11
1.13
0.69
1.13

4,836,185
703,401
7,250,794
2,968,859
39,034,824
5,707,954
3,516,977
964,590
698,464
21,347,900
10,480,913
1,356,765
1,790,518
12,451,406
6,657,419
3,116,100
2,851,117
4,385,967
4,537,420
1,331,924
5,951,913
6,831,799
9,883,888
5,604,353
2,902,505
6,035,560

Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming

Factor

Population

0.21
0.52
0.77
0.33
1.15
0.51
1.19
1.18
0.17
1.10
1.06
1.07
1.11
0.28
1.07
0.22
1.10
1.32
0.53
0.18
1.19
1.18
0.48
1.13
0.16

1,058,638
1,910,003
3,077,543
1,348,147
8,780,729
2,062,715
19,173,378
10,353,123
748,215
11,524,840
3,886,392
4,201,503
12,603,961
1,044,437
5,093,995
870,562
6,758,728
28,763,793
3,214,318
617,810
8,345,522
7,564,480
1,755,736
5,762,472
569,502

Source: U.S. Census Bureau, Current Population Survey, Internal data files for the 2010 Design; U.S. Census
Bureau, Population Estimates, March 2020.
Notes: The state population counts in this table are for the 0+ population. For same-sex households,
multiply the a- and b-parameters by 1.3. For foreign-born and noncitizen characteristics for Total
and White, the a- and b-parameters should be multiplied by 1.3. No adjustment is necessary for
foreign-born and noncitizen characteristics for Black, Asian, American Indian and Alaska Native,
Native Hawaiian and Other Pacific Islander, and Hispanic.

SOURCE & ACCURACY

G-39

Table 24. Factors and Populations for Regional Standard Errors and Parameters: 2020 Annual
Social and Economic Supplement
Region
Midwest
Northeast
South
West

Factor
1.06
1.07
1.13
1.12

Population
67,415,935
55,249,162
124,032,005
77,592,955

Source: U.S. Census Bureau, Current Population Survey, Internal data files for the 2010 Design; U.S. Census
Bureau, Population Estimates, March 2020.
Notes: The state population counts in this table are for the 0+ population. For same-sex households, multiply the aand b-parameters by 1.3. For foreign-born and noncitizen characteristics for Total and White, the a- and bparameters should be multiplied by 1.3. No adjustment is necessary for foreign-born and noncitizen
characteristics for Black, Asian, American Indian and Alaska Native, Native Hawaiian and Other Pacific
Islander, and Hispanic.

G-40

SOURCE & ACCURACY

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U.S. Census Bureau. (2019a). 2017 CPS ASEC Research Files. https://www.census.
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gov/data/datasets/2018/demo/income-poverty/cps-asec-bridge.html

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All online references accessed August 7, 2020.

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SOURCE & ACCURACY